**Purpose**

To generate orthogonal symplectic matrices U or V, defined as products of symplectic reflectors and Givens rotations U = diag( HU(1),HU(1) ) GU(1) diag( FU(1),FU(1) ) diag( HU(2),HU(2) ) GU(2) diag( FU(2),FU(2) ) .... diag( HU(n),HU(n) ) GU(n) diag( FU(n),FU(n) ), V = diag( HV(1),HV(1) ) GV(1) diag( FV(1),FV(1) ) diag( HV(2),HV(2) ) GV(2) diag( FV(2),FV(2) ) .... diag( HV(n-1),HV(n-1) ) GV(n-1) diag( FV(n-1),FV(n-1) ), as returned by the SLICOT Library routines MB04TS or MB04TB. The matrices U and V are returned in terms of their first N/2 rows: [ U1 U2 ] [ V1 V2 ] U = [ ], V = [ ]. [ -U2 U1 ] [ -V2 V1 ]

SUBROUTINE MB04WR( JOB, TRANS, N, ILO, Q1, LDQ1, Q2, LDQ2, CS, $ TAU, DWORK, LDWORK, INFO ) C .. Scalar Arguments .. CHARACTER JOB, TRANS INTEGER ILO, INFO, LDQ1, LDQ2, LDWORK, N C .. Array Arguments .. DOUBLE PRECISION CS(*), DWORK(*), Q1(LDQ1,*), Q2(LDQ2,*), TAU(*)

**Input/Output Parameters**

JOB CHARACTER*1 Specifies whether the matrix U or the matrix V is required: = 'U': generate U; = 'V': generate V. TRANS CHARACTER*1 If JOB = 'U' then TRANS must have the same value as the argument TRANA in the previous call of MB04TS or MB04TB. If JOB = 'V' then TRANS must have the same value as the argument TRANB in the previous call of MB04TS or MB04TB. N (input) INTEGER The order of the matrices Q1 and Q2. N >= 0. ILO (input) INTEGER ILO must have the same value as in the previous call of MB04TS or MB04TB. U and V are equal to the unit matrix except in the submatrices U([ilo:n n+ilo:2*n], [ilo:n n+ilo:2*n]) and V([ilo+1:n n+ilo+1:2*n], [ilo+1:n n+ilo+1:2*n]), respectively. 1 <= ILO <= N, if N > 0; ILO = 1, if N = 0. Q1 (input/output) DOUBLE PRECISION array, dimension (LDQ1,N) On entry, if JOB = 'U' and TRANS = 'N' then the leading N-by-N part of this array must contain in its i-th column the vector which defines the elementary reflector FU(i). If JOB = 'U' and TRANS = 'T' or TRANS = 'C' then the leading N-by-N part of this array must contain in its i-th row the vector which defines the elementary reflector FU(i). If JOB = 'V' and TRANS = 'N' then the leading N-by-N part of this array must contain in its i-th row the vector which defines the elementary reflector FV(i). If JOB = 'V' and TRANS = 'T' or TRANS = 'C' then the leading N-by-N part of this array must contain in its i-th column the vector which defines the elementary reflector FV(i). On exit, if JOB = 'U' and TRANS = 'N' then the leading N-by-N part of this array contains the matrix U1. If JOB = 'U' and TRANS = 'T' or TRANS = 'C' then the leading N-by-N part of this array contains the matrix U1**T. If JOB = 'V' and TRANS = 'N' then the leading N-by-N part of this array contains the matrix V1**T. If JOB = 'V' and TRANS = 'T' or TRANS = 'C' then the leading N-by-N part of this array contains the matrix V1. LDQ1 INTEGER The leading dimension of the array Q1. LDQ1 >= MAX(1,N). Q2 (input/output) DOUBLE PRECISION array, dimension (LDQ2,N) On entry, if JOB = 'U' then the leading N-by-N part of this array must contain in its i-th column the vector which defines the elementary reflector HU(i). If JOB = 'V' then the leading N-by-N part of this array must contain in its i-th row the vector which defines the elementary reflector HV(i). On exit, if JOB = 'U' then the leading N-by-N part of this array contains the matrix U2. If JOB = 'V' then the leading N-by-N part of this array contains the matrix V2**T. LDQ2 INTEGER The leading dimension of the array Q2. LDQ2 >= MAX(1,N). CS (input) DOUBLE PRECISION array, dimension (2N) On entry, if JOB = 'U' then the first 2N elements of this array must contain the cosines and sines of the symplectic Givens rotations GU(i). If JOB = 'V' then the first 2N-2 elements of this array must contain the cosines and sines of the symplectic Givens rotations GV(i). TAU (input) DOUBLE PRECISION array, dimension (N) On entry, if JOB = 'U' then the first N elements of this array must contain the scalar factors of the elementary reflectors FU(i). If JOB = 'V' then the first N-1 elements of this array must contain the scalar factors of the elementary reflectors FV(i).

DWORK DOUBLE PRECISION array, dimension (LDWORK) On exit, if INFO = 0, DWORK(1) returns the optimal value of LDWORK. On exit, if INFO = -12, DWORK(1) returns the minimum value of LDWORK. LDWORK INTEGER The length of the array DWORK. LDWORK >= MAX(1,2*(N-ILO+1)). If LDWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the DWORK array, returns this value as the first entry of the DWORK array, and no error message related to LDWORK is issued by XERBLA.

INFO INTEGER = 0: successful exit; < 0: if INFO = -i, the i-th argument had an illegal value.

[1] Benner, P., Mehrmann, V., and Xu, H. A numerically stable, structure preserving method for computing the eigenvalues of real Hamiltonian or symplectic pencils. Numer. Math., Vol 78 (3), pp. 329-358, 1998. [2] Kressner, D. Block algorithms for orthogonal symplectic factorizations. BIT, 43 (4), pp. 775-790, 2003.

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**Program Text**

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